What is the Greatest Common Factor of 31590 and 31600?

Greatest common factor (GCF) of 31590 and 31600 is 10.

GCF(31590,31600) = 10

We will now calculate the prime factors of 31590 and 31600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31590 and 31600.

How to find the GCF of 31590 and 31600?

We will first find the prime factorization of 31590 and 31600. After we will calculate the factors of 31590 and 31600 and find the biggest common factor number .

Step-1: Prime Factorization of 31590

Prime factors of 31590 are 2, 3, 5, 13. Prime factorization of 31590 in exponential form is:

31590 = 2¹ × 3⁵ × 5¹ × 13¹

Step-2: Prime Factorization of 31600

Prime factors of 31600 are 2, 5, 79. Prime factorization of 31600 in exponential form is:

31600 = 2⁴ × 5² × 79¹

Step-3: Factors of 31590

List of positive integer factors of 31590 that divides 31590 without a remainder.

1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 27, 30, 39, 45, 54, 65, 78, 81, 90, 117, 130, 135, 162, 195, 234, 243, 270, 351, 390, 405, 486, 585, 702, 810, 1053, 1170, 1215, 1755, 2106, 2430, 3159, 3510, 5265, 6318, 10530, 15795

Step-4: Factors of 31600

List of positive integer factors of 31600 that divides 31590 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 79, 80, 100, 158, 200, 316, 395, 400, 632, 790, 1264, 1580, 1975, 3160, 3950, 6320, 7900, 15800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31590 and 31600. The biggest common factor number is the GCF number.
So the greatest common factor 31590 and 31600 is 10.

Also check out the Least Common Multiple of 31590 and 31600